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Matched Asymptotic Expansions in Reaction-Diffusion Theory / Edition 1

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This volume contains a wealth of results and methodologies applicable to a wide range of problems arising in reaction-diffusion theory. It can be viewed both as a handbook, and as a detailed description of the methodology. The authors present new methods based on matched asymptotic expansions.

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Editorial Reviews

From the Publisher

From the reviews of the first edition:

"The book contains useful information on the topic, especially precise (and non-standard) asymptotic expansions in different regions collected with the help of the MAE-s into the complete characterization of the solutions to the nonlinear problems in consideration. The book is warmly recommended to specialists in ODE-s, PDE-s, researchers in reaction-diffusion theory, physicists, engineers and to students with basic knowledge on parabolic equations." (Jeno Hegedus, Acta Scientiarum Mathematicarum, Vol. 72, 2006)

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Product Details

  • ISBN-13: 9781852337674
  • Publisher: Springer London
  • Publication date: 9/1/2010
  • Series: Springer Monographs in Mathematics Series
  • Edition description: 2004
  • Edition number: 1
  • Pages: 290
  • Product dimensions: 0.69 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

Pt. I The Evolution of Travelling Waves in Scalar Fisher-Kolmogorov Equations
1 Introduction 3
2 Generalized Fisher Nonlinearity 15
3 mth-Order (m > 1) Fisher Nonlinearity: Initial Data with Exponential Decay Rates or Compact Support 39
4 mth-Order (m > 1) Fisher Nonlinearity: Initial Data with Algebraic Decay Rates 75
5 Extension to Systems of Fisher-Kolmogorov Equations. Example: A Simple Model for an Ionic Autocatalytic System 111
Pt. II The Analysis of a Class of Singular Scalar Reaction-Diffusion Equations
6 Introduction 151
7 Permanent Form Travelling Waves (PTWs) 155
8 The Initial-Boundary Value Problem 177
9 Asymptotic Solution of IBVP as [actual symbol not reproducible] Initial Data with Exponential or Algebraic Decay Rates 213
10 Extension to the System of Singular Reaction-Diffusion Equations 221
A Construction of a Global Nonnegative Solution to the Scalar Equation [omega][subscript t] = [omega][subscript xx] + [mu][superscript *] [omega][superscript n] 271
B Asymptotic Solutions to the Eigenvalue Problem (8.68)-(8.71) as [actual symbol not reproducible] 273
C Analysis of Boundary Value Problem (8.76)-(8.78) 277
D Analysis of Boundary Value Problem (8.90)-(8.92) 281
References 283
Index 289
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